Reqsubsets results differ with coef() for model with linear dependencies - r

Question

while using Regsubsets from package leaps on data with linear dependencies, I found that results given by coef() and by summary()$which differs. It seems that, when linear dependencies are found, reordering changes position of coefficients and coef() returns wrong values.
I use mtcars just to "simulate" the problem I had with other data. In first example there is no issue of lin. dependencies and best given model by BIC is mpg~wt+cyl and both coef(),summary()$which gives the same result. In second example I add dummy variable so there is possibility of perfect multicollinearity, but variables in this order (dummy in last column) don't cause the problem. In last example after changing order of variables in dataset, the problem finally appears and coef(),summary()$which gives different models. Is there anything incorrect in this approach? Is there any other way to get coefficients from regsubsets?
require("leaps") #install.packages("leaps")
###Example1
dta <- mtcars[,c("mpg","cyl","am","wt","hp") ]
bestSubset.cars <- regsubsets(mpg~., data=dta)
(best.sum <- summary(bestSubset.cars))
#
w <- which.min(best.sum$bic)
best.sum$which[w,]
#
best.sum$outmat
coef(bestSubset.cars, w)
#
###Example2
dta2 <- cbind(dta, manual=as.numeric(!dta$am))
bestSubset.cars2 <- regsubsets(mpg~., data=dta)
(best.sum2 <- summary(bestSubset.cars2))
#
w <- which.min(best.sum2$bic)
best.sum2$which[w,]
#
coef(bestSubset.cars2, w)
#
###Example3
bestSubset.cars3 <- regsubsets(mpg~., data=dta2[,c("mpg","manual","am","cyl","wt","hp")])
(best.sum3 <- summary(bestSubset.cars3))
#
w <- which.min(best.sum3$bic)
best.sum3$which[w,]
#
coef(bestSubset.cars3, w)
#
best.sum2$which
coef(bestSubset.cars2,1:4)
best.sum3$which
coef(bestSubset.cars3,1:4)

Answer 1

The order of vars by summary.regsubsets and regsubsets are different. The generic function coef() of regsubsets calls those two in one function, and the results are in mess if you are trying to force.in or using formula with fixed order. Changing some lines in the coef() function might help. Try codes below, see if it works!
coef.regsubsets <- function (object, id, vcov = FALSE, ...)
{
s <- summary(object)
invars <- s$which[id, , drop = FALSE]
betas <- vector("list", length(id))
for (i in 1:length(id)) {
# added
var.name <- names(which(invars[i, ]))
thismodel <- which(object$xnames %in% var.name)
names(thismodel) <- var.name
# deleted
#thismodel <- which(invars[i, ])
qr <- .Fortran("REORDR", np = as.integer(object$np),
nrbar = as.integer(object$nrbar), vorder = as.integer(object$vorder),
d = as.double(object$d), rbar = as.double(object$rbar),
thetab = as.double(object$thetab), rss = as.double(object$rss),
tol = as.double(object$tol), list = as.integer(thismodel),
n = as.integer(length(thismodel)), pos1 = 1L, ier = integer(1))
beta <- .Fortran("REGCF", np = as.integer(qr$np), nrbar = as.integer(qr$nrbar),
d = as.double(qr$d), rbar = as.double(qr$rbar), thetab = as.double(qr$thetab),
tol = as.double(qr$tol), beta = numeric(length(thismodel)),
nreq = as.integer(length(thismodel)), ier = numeric(1))$beta
names(beta) <- object$xnames[qr$vorder[1:qr$n]]
reorder <- order(qr$vorder[1:qr$n])
beta <- beta[reorder]
if (vcov) {
p <- length(thismodel)
R <- diag(qr$np)
R[row(R) > col(R)] <- qr$rbar
R <- t(R)
R <- sqrt(qr$d) * R
R <- R[1:p, 1:p, drop = FALSE]
R <- chol2inv(R)
dimnames(R) <- list(object$xnames[qr$vorder[1:p]],
object$xnames[qr$vorder[1:p]])
V <- R * s$rss[id[i]]/(object$nn - p)
V <- V[reorder, reorder]
attr(beta, "vcov") <- V
}
betas[[i]] <- beta
}
if (length(id) == 1)
beta
else betas
}

Answer 2

Another solution that works for me is to randomize the order of the column(independent variables) in your dataset before running the regsubsets. The idea is that after reorder hopefully the highly correlated columns will be far apart from each other and will not trigger the reorder behavior in the regsubsets algorithm.